Question

How do I figure this out?

Answer 1

`\mathrm{The\ second\ and\ fourth\ option\ is\ correct.}\\`

Step-by-step explanation:

`\mathrm{In\ the\ first\ option,\ triangles\ A\ and\ B\ each\ have\ a\ 51^o\ angle,\ but\ they\ may\ have\ }\\\mathrm{different\ angle\ measures\ for\ other\ two\ angles.\ So,\ this\ does\ not\ satisfy\ AA}\\\mathrm{similarity\ axiom.}`

`\mathrm{In\ the\ second\ option,\ isosceles\ triangles\ C\ and\ D\ each\ have\ a\ 50^o\ angle,\ which}\\\mathrm{means\ each\ of\ them\ has\ other\ two\ equal\ angles,\ i.e.\ 65^o\ each.\ This\ makes\ all\ of}\\\mathrm{the\ corresponding\ angles\ of\ the\ triangles\ equal,\ hence\ they\ are\ similar.}`

`\mathrm{In\ the\ third\ option,\ triangle\ E\ has\ a\ 20^o\ angle\ and\ a\ 70^o\ angle.\ This\ means\ the\ }\\\mathrm{third\ angle\ must\ be\ 90^o.\ And,\ triangle\ F\ has\ a\ 60^o\ angle\ and\ a\ 20^o\ angle.\ That}\\\mathrm{means,\ the\ third\ angle\ now\ is\ 100^o.\ So\ the\ corresponding\ angles\ are\ not\ equal\ }\\\mathrm{in\ these\ triangles.\ So\ they\ are\ not\ similar.}`

`\mathrm{In\ fourth\ option,\ triangle\ G\ has\ a\ 40^o\ angle\ and\ a\ 35^o\ angle.\ This\ means}\\\mathrm{the\ third\ angle\ of\ this\ triangle\ is\ 105^o.\ And\ triangle\ H\ has\ a\ 40^o\ angle\ and\ a}\\\mathrm{105^o\ angle.\ So\ the\ third\ angle\ is\ 35^o.\ Notice,\ triangle\ G\ has\ three\ angles: }\\\mathrm{40^o,\ 35^o\ and\ 105^o.\ Triangle\ H\ also\ has\ the\ same\ angles.\ Hence\ they\ are \ similar. }`